Smoking in your Grill is easier than you think but to get a really good result there are a few things to remember.
This is how I play my Weber 57cm Grill (See picture below)
Place the lit briquettes on one side of the Grill.
Place a Smokebox filled with Woodchips (dry not wet) directly on top of the lit briquettes.
Put on the grid.
Place the Food on the opposite side of the Grill from the briquettes.
Put the lid on the grill but with the Vents on the lid fully opened and right above the Food.
This way the heat and smoke will go straight over the Food on its way out of the Vents
and you get a really Good Smoke!